CN105373653B - A kind of localization method of large scale weak separation Thin-shell workpiece - Google Patents
A kind of localization method of large scale weak separation Thin-shell workpiece Download PDFInfo
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- CN105373653B CN105373653B CN201510703877.1A CN201510703877A CN105373653B CN 105373653 B CN105373653 B CN 105373653B CN 201510703877 A CN201510703877 A CN 201510703877A CN 105373653 B CN105373653 B CN 105373653B
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- G06—COMPUTING; CALCULATING OR COUNTING
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Abstract
The invention discloses a kind of localization methods of large scale weak separation Thin-shell workpiece, include the following steps：First to meet workpiece clamp holding force demand as target, and based on workpiece configurations positioning accuracy, anchor point quantity and its geometrical interference constraint, preferentially anchor point is added in machining area, it realizes and targetedly emphasis prevention and control is implemented to the position error of workpiece difference machining area, required anchor point quantity is determined with this, and then by way of following each machining area maximum positioning error location arrangements anchor point of workpiece, the search of the more anchor point initial layouts of workpiece is completed.Secondly, use for reference susceptibility concept, build the susceptibility expression formula of work pieces process deformation relative positioning point layout, the workpiece anchor point for reducing machining deformation by search is laid out most sensitive adjustment direction, workpiece anchor point layout optimization decision is obtained with this, its optimization process is expressed as the more anchor points for being intended to reduce machining deformation simultaneously and coordinates and optimizes problem, and constructs the Optimizing Flow that adjustment anchor point layout approaches the deformation of workpiece minimum process, realizes the optimization to the more anchor point initial layouts of workpiece；Finally, by designing mode experiment, modal parameter of the extraction work clipping system under more anchor points optimization layout is adjusted the more anchor point layouts of workpiece after optimization, or continues to add auxiliary positioning point, further improves workpiece processing quality from the angle of vibration suppression.
Description
Technical field
The present invention relates to a kind of localization methods of large scale weak separation Thin-shell workpiece, are used for large scale weak separation Thin-shell
The optimization of workpiece multipoint positioning parameter.
Background technology
The Thin-shells workpiece such as large scale alloy or composite material thin wall part, is commonly used for the exterior skin of modern Large Scale Space Vehicle,
Its manufacturing process generally uses " first processing aftershaping " technique, but its molding procedure frequently can lead to the outer profile of machined part
Large deformation is generated, the aeroperformance and Stealth Fighter of aircraft are easily influenced.
In order to overcome the problems referred above, it " is first molded post-processing " technique is gradually applied, but semi-finished product category weak separation after molding
Thin-shell Part, positioning difficulty increase, and " 3-2-1 " six independent positioning method towards rigid body is no longer applicable in.In consideration of it,
" N-2-1 " location technology is suggested, and can weaken deformation of the workpiece in the technical process such as measurement and milling groove, but can not press down
The phenomenon that machining area rigidity in the technical process such as trimming processed caused by local positioning point failure weakens；For this purpose, " X-2-1 " is dynamic
State localization method is suggested, but it is also in the conceptual description stage, less for the technological accumulation of " how finding optimal X ".
Traditional fixture scheme determines the accumulation dependent on intuitive judgment and experience, or targetedly weak to workpiece rigid
Degree position is reinforced.It has a disadvantage in that：1. the acquisition of experience continuous development of the generation to processing quality not in time；2. weak separation portion
The specific aim reinforcing of position need to be attempted and be adjusted for a long time.For this purpose, a large amount of technological development is around the more anchor point layouts of workpiece
Optimization method expansion, but coincidentally selective positioning precision is deformed into workpiece to most of method proposed with machining path
The target of anchor point layout optimization, but entire optimization process known to workpiece anchor point initial layout under the conditions of carry out, so
And exactly the acquisition of workpiece oplimal Location point layout is to its initial layout, i.e. the initial value quite sensitive of optimization process.
It is also easy to produce machining deformation and the low fact of location efficiency, large scale weak separation Thin-shell work based on conventional mapping methods
The localization method of part has become industrial quarters and more likes and concerned issue.Therefore, workpiece anchor point quantity how is determinedHow to search
Rope workpiece anchor point is laid outIt improves large scale weak separation Thin-shell workpiece processing quality to be short of, while its research is also
Lag.
Invention content
The object of the present invention is to provide a kind of localization methods of large scale weak separation Thin-shell workpiece, and this method solve this
The complete positional parameter of class workpiece, includes the select permeability of anchor point quantity, position, cracked workpiece anchor point quantity, layout with
Internal association between its positioning accuracy, machining deformation and clamping stability.
The technical solution of invention is：
(1) chucking power is selected to ensure workpiece positioning completely index the most direct and important, that is, to optimize with machining deformation
Target, value range can consult mechanical workshop manual according to Thin-shell workpiece model and calculate acquisition.
(2) quantity and its initial layout of workpiece anchor point are determined.
It is several processing and non-processing region to divide its finished surface along work pieces process path, is to meet workpiece clamp holding force
Target, and based on the constraints of geometrical interference between anchor point total resources and anchor point, preferentially add and position in machining area
Point；After reaching workpiece to the demand of chucking power, anchor point is further added, to improve workpiece configurations positioning accuracy, until determining
Actually required anchor point quantity.
It selects each machining area maximum positioning error of workpiece position to add anchor point, determines the opposite of all anchor points of workpiece
Position obtains with this while meeting the workpiece initial alignment scheme of chucking power and positioning accuracy demand, i.e.,：More anchor points of workpiece
Initial layout.
(3) optimisation strategy of the more anchor point initial layouts of workpiece is designed.
It is inspired by plant growth competition rule, in conjunction with susceptibility concept, relatively each positioning of work pieces process deformation is compared in calculating
Point along different directions unit quantity move after change rate, searched for this can quickly reduce work pieces process deformation most sensitive anchor point
And its position adjustment direction, the adjustable strategies that should be followed in the more anchor point layout optimization process of workpiece are ultimately generated, i.e.,：Adjust phase
Anchor point is answered to be moved along the most sensitive direction for reducing work pieces process deformation.
For ease of calculating, above-mentioned optimisation strategy is constructed using central difference schemes, mathematic(al) representation is：
In formula, SxIndicate that the machining deformation of workpiece moves the sensitivity of increment with anchor point along tooling X-axis while Moving Unit
Degree；PiIndicate space of each slide positioning unit end anchor point in tooling coordinate system on workpiece No. i-th ram of positioning tool
Coordinates matrix, i=1~m, m indicate the quantity of tooling upper ram；Pi+With f (Pi+) workpiece No. i-th cunning of positioning tool is indicated respectively
Each slide positioning unit end anchor point moves increment Delta p along tooling X-axis positive direction Moving Unit on pillowxAll anchor points afterwards
The maximum machining deformation of workpiece, P under layout and the layouti+=(P1,P2,…,Pi+(Δpx 0 0)T,…,Pm)；Pi-With f (Pi-)
Indicate that each slide positioning unit end anchor point moves list along tooling X-axis negative direction on workpiece No. i-th ram of positioning tool respectively
Increment Delta p is moved in displacementxThe maximum machining deformation of workpiece, P under all anchor points layout and the layout afterwardsi-=(P1,P2,…,Pi-
(Δpx 0 0)T,…,Pm)；SyIndicate that the machining deformation of workpiece moves the sensitivity of increment with anchor point along tooling Y-axis Moving Unit
Degree；pi,jIndicate that jth slide positioning unit end anchor point is in tooling coordinate system on workpiece No. i-th ram of positioning tool
Space coordinate vector, j=1~n, n indicate the quantity of each ram upper saddle of tooling；Pi,j+With f (Pi,j+) indicate that workpiece is fixed respectively
Jth slide positioning unit end anchor point moves increment Delta along tooling Y-axis positive direction Moving Unit on No. i-th ram of tooling of position
pyThe maximum machining deformation of workpiece, P under all anchor points layout and the layout afterwardsi,j+=(P1,P2,…,Pi j+,…,Pm), Pi j+
=(pi,1,pi,2,…,pi,j+(0 Δpy 0)T,…,pi,n)；Pi,j-With f (Pi,j-) workpiece No. i-th cunning of positioning tool is indicated respectively
Jth slide positioning unit end anchor point moves increment Delta p along tooling Y-axis negative direction Moving Unit on pillowyAfterwards all fixed
The maximum machining deformation of workpiece, P under site layout and the layouti,j-=(P1,P2,…,Pi j-,…,Pm), Pi j-=(pi,1,
pi,2,…,pi,j-(0 Δpy 0)T,…,pi,n)。
(4) optimization algorithm of the more anchor point initial layouts of workpiece is designed.
Mathematic(al) simplification workpiece multipoint positioning tooling prototype, it is optimization aim to select workpiece to resist the ability of machining deformation, together
When in conjunction with the geometrical interference constraint between each anchor point, workpiece more anchor point initial layouts adjustment processes are mathematically represented as being intended to subtract
More anchor points of small machining deformation coordinate and optimize problem, and complete the structure of Optimized model.
The inner link between optimal objective value and restrained boundary is parsed, determines anchor point engineering driving restraint and susceptibility meter
It calculates, structure is intended to the optimization algorithm that the adjustment more anchor point initial layouts of workpiece approach the deformation of workpiece minimum process, is obtained pair with this
Answer the Optimal Stiffness of work pieces process position.
(5) more anchor points optimization layout of workpiece is corrected again.
Mode experiment is designed, the characteristics of mode of more lower work clipping systems of anchor point optimization layout is tested, it is intrinsic that it is disclosed with this
The changing rule of frequency and the vibration shape, and identify the stability of work clipping system.
According to work clipping system modal frequency and vibration shape feature, the locating point position within the scope of big vibration deformation trend is carried out
Fine tuning, or continue to add auxiliary positioning point at maximum vibration trend, Workpiece vibration is inhibited with this, and further improve workpiece and add
Working medium amount.
It the advantage is that：The present invention positions characteristic index structure, positioning completely comprising large scale weak separation Thin-shell workpiece
Point quantity is determining and its initial layout search, the optimisation strategy of more anchor point initial layouts and algorithm design, more anchor points optimize
It is laid out modification method again.On the one hand, the method for following machining area to determine anchor point quantity and its initial layout proposed, has
Conducive to designer under the premise of being clamped reliable in ensureing workpiece process, it is based on limited anchor point number constraint, it is right
The position error of workpiece different zones implements targetedly emphasis prevention and control, and being provided for the layout global optimization of workpiece anchor point can
The optimization initial value leaned on；On the other hand, designed edge reduces the optimization plan of the most sensitive direction adjustment anchor point distribution of machining deformation
Summary and flow have cracked the internal association between workpiece anchor point layout and machining deformation, realize workpiece anchor point layout
Global optimization；In addition, workpiece more anchor points optimization layout is modified according to modal parameter, or addition auxiliary positioning point, into
Angle of one step based on vibration suppression improves work pieces process processing quality.
Description of the drawings
Fig. 1 type free form surface aircraft skin exemplars；
The finite element numerical analysis model of Fig. 2 workpiece multipoint positionings；
The quantity determination and the search of initial layout of Fig. 3 workpiece anchor points；
The variation course of Fig. 4 workpiece clamp holding force summations；
The variation course of each machining area maximum positioning error of Fig. 5 workpiece；
The multipoint positioning tooling prototype of Fig. 6 large scale weak separation Thin-shell workpiece；
The simplified model of Fig. 7 large scale weak separation Thin-shell workpiece multipoint positioning tooling prototypes；
The Optimizing Flow of the more anchor point initial layouts of Fig. 8 workpiece：Adjusting stage I；
The Optimizing Flow of the more anchor point initial layouts of Fig. 9 workpiece：Adjusting stage II；
The Optimizing Flow of the more anchor point initial layouts of Figure 10 workpiece：Adjusting stage III；
The Optimizing Flow of the more anchor point initial layouts of Figure 11 workpiece：Adjusting stage XIII；
The front and back machining deformation of the more anchor point initial layout optimizations of Figure 12 workpiece compares；
The variation course of Figure 13 workpiece maximum machining deformations and rigidity；
The mode experiment of Figure 14 work clipping systems tests system；
1 rank Mode Shape of Figure 15 workpiece.
Specific implementation mode
See Fig. 1~Figure 14, according to the structural symmetry of certain type free form surface aircraft skin, Fig. 1 shows the four of the workpiece
/ part, and its finished surface is divided into several machining areas and non-processing region along machining path 1,2, such as：Processing
Region 1~4.The addition of anchor point is preferentially carried out in each machining area of workpiece.
Fig. 2 constructs workpiece multipoint positioning finite element numerical analysis model, for being positioned in workpiece anchor point adding procedure
The calculating of machining deformation in the calculating of error and workpiece anchor point initial layout optimization process.
The a quarter symmetric part that Fig. 3 has chosen workpiece as shown in Figure 1 is analysis object, illustrates workpiece positioning points
The determination of amount and the search process of initial layout experienced 7 additions altogether.Wherein, it is work that identifier, which is the anchor point of " (0) ",
The initial positioning method of part；" (1) " indicates to add positioning in the maximum positioning error position of machining area 1~4 respectively the 1st time
The meaning of point, other localization point identifiers number is similar.
Fig. 4 illustrates the variation course of chucking power summation in the adding procedure of workpiece anchor point shown in Fig. 3.Wherein, anchor point
After 6 additions, chucking power summation FJ1425N is reached, has met workpiece clamp holding force demand, therefore opened from the 7th addition of anchor point
Begin, further considers whether Workpiece's Tack Error meets its shape positioning accuracy.
Fig. 5 illustrates the variation course of each machining area maximum positioning error in the adding procedure of workpiece anchor point shown in Fig. 3.
Wherein, under the premise of meeting workpiece clamp holding force demand, the maximum positioning error of machining area 2 is found in the 7th adding procedure
δ2_max(+0.0871mm) meets workpiece configurations required precision δmax(± 0.1mm), and the maximum positioning error in machining area 1
δ1_max(+0.1503mm) is but unsatisfactory for, therefore the 7th addition only selects to carry out in machining area 1, while anchor point quantity reaches
Limit Nmax=20, therefore anchor point adding procedure terminates.
Fig. 6 is according to typical large scale weak separation Thin-shell workpiece --- and the architectural characteristic of single-curved surface aircraft skin constructs
The tooling prototype of its multipoint positioning, use positioning lattice array tooling X and Y coordinates concentrate adjustment, Z coordinate individually adjust and
The mode of unilateral vacuum chuck positioning.Major parameter is：Position radius of a ball r=20mm, sucker diameter r=80mm, ram number m=
10, the positioning unit number n=2 on each ram, the minimum spacing limiting value of anchor point on adjacent 2 rams in X-direction
Dxmin=150mm, the minimum spacing limiting value D of adjacent 2 anchor points in the Y direction on same ramymin=150mm.
Fig. 7 is the simplified model of the multipoint positioning tooling prototype of large scale weak separation Thin-shell workpiece shown in Fig. 6, right with this
Workpiece resists the ability of machining deformation, the constraint of anchor point geometrical interference and its initial layout optimisation strategy and carries out mathematical description, and
The more anchor point initial layout adjustment processes of workpiece are mathematically represented as the more anchor points for being intended to reduce machining deformation coordination optimization to ask
Topic, completes the design of the structure and algorithm of Optimized model.
Fig. 8~Figure 11 illustrates the optimization process of workpiece anchor point initial layout, and identifies the adjustment road of anchor point
Diameter.Wherein, solid line indicates that blank profile, dotted line indicate that machining path, black circle indicate that anchor point, " " indicate machining path
Maximum distortion position, arrow indicate to move corresponding anchor point, " S-Y to direction:1 " indicates that the 1st step of optimization process is pair
Adjustment of the anchor point along Y-axis is answered,Indicate the maximum machining deformation position after the 1st successive step, " S-X:1 " withAnd it is other similar.
The processing that Figure 12 optimizes each discrete point position on front and back machining path 1,2 than right workpiece anchor point initial layout becomes
Shape.Wherein, the machining deformation in path 1 greatly reduces after optimization, and the machining deformation in path 2 is basically unchanged, main reason is that：
Compared with path 1, the positioning dot density bigger around path 2 directly ensures that maximum machining deformation does not appear at path 2,
Therefore optimization process does not select to adjust surrounding anchor point.
Figure 13 illustrates maximum machining deformation and follows dynamic stiffness with the variation tendency of adjustment number, it is seen that maximum processing becomes
Shape substantially increases the rigidity of workpiece process than reducing 34.5% before optimization.
Figure 14 is that the mode experiment of work clipping system tests system, is optimized in more anchor points for obtaining workpiece under extraneous exciting
The dynamic response signal of layout, and complete the functions such as filtering, amplification and the parameter identification of signal, final identification work clipping system
Characteristics of mode.
Figure 15 illustrates 1 rank Mode Shape of workpiece, it is found that the workpiece entirety vibration shape is " bending+distortion ", and intermediate without fixed
The non-processing region in site produces bending vertically, it means that：Only extremely along the length and width direction of workpiece
It is respectively arranged a pair of of auxiliary positioning point less, could play inhibiting effect to the flexural deformation and torsional deflection of workpiece.
Embodiment 1
Here with certain type single-curved surface aircraft skin, appearance and size is 1920mm × 1320mm, thickness 3mm, and material is
7075 aluminium alloys, elastic modulus Ewp=70GP need to control shape position error δmaxNo more than ± 0.1mm, and process all cinctures
Exterior feature opens two rectangular windows, for applying 300N cutting force successively along machining path, illustrates large scale weak separation Thin-shell workpiece
The optimization process of more positional parameters.
(1) index that structure characterization large scale weak separation Thin-shell workpiece positions completely.
The characteristic index for selecting workpiece clamp holding force to be positioned completely for guarantee workpiece with machining deformation, and it is large-scale with reference to aviation class
Thin-wall workpiece frequently with unilateral vacuum chuck support pattern, Workpiece clamping frictional force and cutting force are compared by formula (1), determine
The size of required chucking power；Wherein, the determination of workpiece cutting force tangential component can pass through access《Mechanical technology handbook》It solves, work
Part grip friction power can be calculated by formula (2) and be obtained.
G=Qf ＞ F (1)
In formula, Q is workpiece clamp holding force, and f is the friction coefficient of piece-holder position, and F is the tangential component of cutting force.
Q=pS (2)
In formula, p is vacuum pressure, and S is effective contact area of piece-holder position.
Thus it can determine, 5600N chucking powers need to be provided for the workpiece in the example.
(2) each machining area of workpiece is followed to determine anchor point quantity and its initial layout.
1) it is processing district and non-processing region to divide workpiece machining surface：As shown in Figure 1, according to certain type single described in example
Work mounting s face is divided into 1,2,3,4 and of machining area by face aircraft skin exemplar structure and processing request along machining path 1,2
Other non-processing regions.
2) the finite element numerical analysis model of workpiece configurations position error is built：According to certain type single-curved surface aircraft described in example
The structural symmetry of covering exemplar, it is analysis object to take its a quarter, non linear finite element analysis technology is based on, with Shell
181 shell units build workpiece multipoint positioning finite element numerical analysis model, as shown in Figure 2.
3) mathematical description of the determination of workpiece anchor point quantity and its initial layout search problem：Based on inventive technique scheme
(2) thinking described in, will " the problem of following work pieces process region to determine anchor point quantity and initial layout is described as --- and it is total fixed
Position resource NmaxConstraint under, solve each machining area of workpiece anchor point quantity and its placement scheme, i.e., each locating point position
P1, P2..., reach workpiece to chucking power demand FJ_maxUnder the premise of, weaken workpiece deformation, it is fixed to control workpiece configurations with this
Position error delta.That is,
Object function：Min (δ)=f (P1, P2...)
Constraints：N≤Nmax, FJ≥FJ_min
The detailed process for solving the above problem is as follows：
Step 1：Initialize installation.
1. the maximum anchor point quantity of setting, Nmax；
2. anchor point initial distribution P (P are arranged1, P2... PN), N=4；
3. it is n machining area to follow machining path to divide work mounting s face.
Step 2：Structure is based on anchor point distribution P (P1, P2... PN) workpiece configurations position error finite element numerical analysis
Model.
Step 3：It solves and extracts the chucking power summation F being applied on workpieceJWith the maximum positioning error of machining area i
δi_max, i=1~n.
Step 4：Judge whether to meet workpiece clamp holding force demand.
If 1. FJ≥FJ_min, show that workpiece meets chucking power demand, go to Step 5；
If 2. FJ＜ FJ_min, show that workpiece is unsatisfactory for chucking power demand, enable N=N+1, and in δi_maxPlace's addition anchor point.
If newly-increased anchor point PNMeet its spacing constraint, it is determined that added in the region, and go to Step 6；Otherwise, it does not add, and enables
N=N-1 goes to Step 6.
Step 5：The anchor point distributed problem solving of machining area i.
If 1. δi_max≤δmax, show to meet the i shape position errors constraint of work pieces process region.I=i+1 is enabled, if i ＞ n,
Show under current anchor point distribution, the analysis of all machining areas has been terminated, and it meets workpiece to chucking power and shape essence
The demand of degree, therefore exit calculating；Otherwise, Step 3 is returned.
If 2. δi_max＞ δmax, show to be unsatisfactory for the i shape position errors constraint of work pieces process region.Enable N=N+1, and
δi_maxPlace's addition anchor point.If newly-increased anchor point PNMeet its spacing constraint, it is determined that added in the region, go to Step 6；
Otherwise, it is not added in the region, and enables N=N-1, go to Step 6.
Step 6：Judge whether to meet maximum anchor point number constraint.
If N ＞ Nmax, show to have exceeded locating resource constraint, exit calculating；Otherwise, i=i+1 is enabled, if i ＞ n, show to work as
Under the distribution of prelocalization point, the analysis of all machining areas is terminated, update anchor point distribution, and has enabled i=1, has returned to Step 2,
Otherwise, Step 3 is returned.
4) result of calculation is analyzed：Fig. 3 shows the search process of the determination of workpiece anchor point quantity and its initial layout.Positioning
Point " (2) " is the 2nd time respectively in the addition of each machining area as a result, similar with the 1st adding procedure, it is assumed that is respectively processed in workpiece
Add anchor point, chucking power summation F in regionJ(600N) is unsatisfactory for workpiece clamp holding force demand FJ_min(1400N), therefore should be each
The addition anchor point of machining area, but in the adding procedure to machining area 4, can not search and meet positioning space constraint
Position.For this purpose, the 2nd adding procedure is not carried out in machining area 4.Similarly, the 5th adding procedure is not in machining area 3
It carries out.After 6th time adds, chucking power summation FJReach 1425N, meets workpiece clamp holding force demand, while it has also been found that machining area 2
Maximum positioning error δ2_max(+0.0871mm) meets workpiece configurations required precision δmax(± 0.1mm), and machining area 1 is most
Big position error δ1_max(+0.1503mm) is but unsatisfactory for, therefore the 7th addition only selects to carry out in machining area 1.Add through 7 times
After adding, anchor point quantity reaches capacity Nmax=20, therefore anchor point adding procedure terminates.About in conjunction with locating point position as shown in Figure 6
Beam is finely adjusted more anchor points layout after adding procedure, obtains workpiece anchor point quantity and its initial layout, position
Point coordinates is as shown in table 1.As shown in Figure 4, Figure 5, workpiece clamp holding force summation FJ(1500N) meet demand, and machining area 1 is most
Big position error δ1_max(+0.1506mm) is still unsatisfactory for requiring, and traces it to its cause and understands：Warpage mainly due to the edge of work is drawn
The large deformation risen, but this partly belongs to blanking part, it is faint on processing quality influence, it can be ignored.
Anchor point space coordinate (the unit of 1 workpiece of table：mm)
(3) the more anchor point initial layout optimisation strategy designs of workpiece for combining susceptibility to calculate.
Susceptibility concept is expressed based on central difference schemes mathematical, in combination with the number of multipoint positioning tooling shown in Fig. 6
Anchor point in simplified model is learned to calculate along the driving direction of X-axis, Y-axis and compare relatively each anchor point unit quantity of work pieces process deformation
Change rate after movement searches for the most sensitive anchor point and its position adjustment direction that can quickly reduce work pieces process deformation with this,
Ultimately generate the adjustable strategies that should be followed in the more anchor point layout optimization process of workpiece；Wherein, the mathematical expression that susceptibility calculates
Formula is：
1. the susceptibility that anchor point moves along the x-axis
In formula, SxIndicate that the machining deformation of workpiece moves the sensitivity of increment with anchor point along tooling X-axis while Moving Unit
Degree；PiIndicate space of each slide positioning unit end anchor point in tooling coordinate system on workpiece No. i-th ram of positioning tool
Coordinates matrix, i=1~m, m indicate the quantity of tooling upper ram；Pi+With f (Pi+) workpiece No. i-th cunning of positioning tool is indicated respectively
Each slide positioning unit end anchor point moves increment Delta p along tooling X-axis positive direction Moving Unit on pillowxAll anchor points afterwards
The maximum machining deformation of workpiece, P under layout and the layouti+=(P1,P2,…,Pi+(Δpx 0 0)T,…,Pm)；Pi-With f (Pi-)
Indicate that each slide positioning unit end anchor point moves list along tooling X-axis negative direction on workpiece No. i-th ram of positioning tool respectively
Increment Delta p is moved in displacementxThe maximum machining deformation of workpiece, P under all anchor points layout and the layout afterwardsi-=(P1,P2,…,Pi-
(Δpx 0 0)T,…,Pm)。
2. the susceptibility that anchor point is moved along Y-axis
In formula, SyIndicate that the machining deformation of workpiece moves the susceptibility of increment with anchor point along tooling Y-axis Moving Unit；
pi,jIndicate space of the jth slide positioning unit end anchor point in tooling coordinate system on workpiece No. i-th ram of positioning tool
Coordinate vector, j=1~n, n indicate the quantity of each ram upper saddle of tooling；Pi,j+With f (Pi,j+) indicate that workpiece positions work respectively
It fills jth slide positioning unit end anchor point on No. i-th ram and moves increment Delta p along tooling Y-axis positive direction Moving UnityAfterwards
All anchor points layout and the layout under workpiece maximum machining deformation, Pi,j+=(P1,P2,…,Pij+,…,Pm), Pi j+=
(pi,1,pi,2,…,pi,j+(0 Δpy 0)T,…,pi,n)；Pi,j-With f (Pi,j-) workpiece No. i-th ram of positioning tool is indicated respectively
Upper jth slide positioning unit end anchor point moves increment Delta p along tooling Y-axis negative direction Moving UnityAll positioning afterwards
The maximum machining deformation of workpiece, P under point layout and the layouti,j-=(P1,P2,…,Pij-,…,Pm), Pi j-=(pi,1,
pi,2,…,pi,j-(0 Δpy 0)T,…,pi,n)。
(4) optimization algorithm of the more anchor point initial layouts of workpiece is constructed.
1) mathematic(al) simplification workpiece multipoint positioning tooling prototype：According to the architectural characteristic of single-curved surface aircraft skin, shown in Fig. 6
Multipoint positioning tooling prototype is described as simplified model as shown in Figure 7.Assuming that it is m, each ram that the system, which has the sum of ram,
With n positioning unit, then arbitrary positioning layout's form is represented by,
P=(P1,P2,…Pm) (5)
In formula, Pi=(pi,1,pi,2,…,pi,n) indicate each slide positioning unit end on workpiece No. i-th ram of positioning tool
Hold space coordinate matrix of the anchor point in tooling coordinate system, i=1,2 ..., m；pi,j=(pi,j_x,pi,j_y,pi,j_z)TFor work
Space coordinate vector of the jth slide positioning unit end anchor point in tooling coordinate system on No. i-th ram of part positioning tool,
J=1,2 ..., n；.Obviously, each anchor point X axis coordinate having the same on same ram.For this purpose, with pi_xIndicate that correspondence is same
Anchor point X-coordinate on ram.In this way, on No. i-th ram on jth slide positioning unit end anchor point space coordinate to
Amount is represented by：
pi,j=(pi_x,pi,j_y,pi,j_z)T (6)
2) ability that design workpiece resists machining deformation is optimization aim：Ensure workpiece reliable retention and meet shape it is fixed
Under the premise of the precision of position, the distribution of adjustment anchor point is improved each on work pieces process path with reducing the deformation of workpiece actual processing with this
The process of rigidity can be expressed as following optimization object function at discrete point position,
max(kD)=f (P1,P2,…,Pm) (7)
In formula, kD=Fp·n/δmN indicates the rigidity of each discrete point position of machining path.If the rigidity very little, table
Deformation is larger at bright corresponding Working position, and processing quality disturbance is big, should adjust anchor point layout, reflect workpiece and accordingly processing
To the desirability of anchor point layout optimization at position.δmFor the machining deformation amount of different location on work pieces process path, FpFor milling
Power is cut, n is the normal vector at each stress point on machining path.
3) workpiece anchor point geometrical interference constraint specification：As shown in fig. 6, to avoid improper anchor point layout is caused from determining
Constructive interference between the clamping device of position, constrains the limit of sports record of each drive component of positioning and clamping mechanism, and main includes sliding
The mobile constraint of pillow and slide, in conjunction with Fig. 7,
1. No. i-th ram is limited along the moving range of X-axis by (i-1)-th, i+1 rams position, i.e.,：
pi-1_x+umin＜ pi_x＜ pi+1_x-uminI=2,3 ... m-1 (8)
In formula, uminMinimum X when being contacted for adjacent ram between the anchor point of corresponding positioning unit end is to spacing.
2. the moving range of two ram of outermost (i=1, m) is limited by fixture system pedestal outer rim X to size, i.e.,：
xmin＜ p1_x＜ p2-x-umin (9)
pm-1-x-umin＜ pm_x＜ xmax (10)
In formula, xmin、xmaxRespectively the 1st, m rams are along the farthest that the positive negative sense of X-axis can be moved to.
3. jth slide on No. i-th ram along Y-axis moving range by bearing/positioning list on jth -1, j+1 slides
The limitation of first present position, i.e.,
pi,j-1_y+vmin<pi,j_y<pi,j+1_y-vminI=1,2 ... m；J=2,3 ... n-1 (11)
In formula, vminThe corresponding minimum Y-direction spacing between bearing/positioning unit end anchor point when being contacted for adjacent slide.
4. the moving range of two slide of outermost (j=1, n) is limited by tool pedestal outer rim Y-direction size, i.e.,：
ymin＜ pi,1_y＜ pi,2_y-vmin (12)
pi,n-1_y-vmin＜ pi,n_y＜ ymax (13)
In formula, ymin、ymaxThe 1st, n slides can be moved to farthest along the positive negative sense of Y-axis on respectively No. i-th ram
Place.
4) the more anchor point initial layout Optimized models of structure workpiece and algorithm flow：Convolution (7)~(13), workpiece is more
Anchor point initial layout adjustment process is mathematically represented as the more anchor points for being intended to reduce machining deformation coordination optimization problem, and completes
The structure of Optimized model, optimization algorithm flow are as follows：
Step 1：Initialize installation.
According to the listed positioning point coordinates of table 1, its initial layout P=(P are set1,P2,…Pm)。
Step 2：It is laid out the finite element modeling of P based on anchor point, solves work pieces process deflection.
Step 3：It solves and follows dynamic stiffness at each discrete Working position in work pieces process path.
1. extracting maximum machining deformation at each discrete Working position of machining path；
2. solving rigidity k at corresponding each discrete Working positionD；
If 3. kD≥kD_max, show that anchor point distribution P meets workpiece processing quality demand, optimization, which calculates, to be terminated；Otherwise,
Anchor point need to be laid out and be adjusted.
Step4：Along Y direction adjustment machining path at maximum machining deformation position around locating point position.
1. with reference to formula (4), the susceptibility S that each anchor point is moved along Y-direction is calculatedy；
2. corresponding anchor point is moved along the most sensitive direction of machining deformation is influenced, if anchor point meets constraints after mobile
(8)~(13), refactoring localization point are laid out P=(P '1,P′2,…,P′m'), return to Step 2；Otherwise, it is held in position a layout P
It is constant, turn to Step 5.
Step5：Along X-direction adjustment machining path at maximum machining deformation position around locating point position.
1. with reference to formula (1), the susceptibility S that each anchor point moves in X direction is calculatedx；
2. corresponding anchor point is moved along the most sensitive direction of machining deformation is influenced, if anchor point meets constraints after mobile
(8)~(13), refactoring localization point are laid out P=(P "1,P″2,…,P″m), return to Step 2；Otherwise, optimization process terminates, and is laid out P
For final optimization pass result.
5) result of calculation is analyzed：Fig. 8 shows that the initial layout of workpiece anchor point, finite element numerical calculate result of calculation table
Bright workpiece maximum machining deformation is happened atPlace, and then it is based on sensitivity analysis, discovery moves along the direction of the arrow in Figure fixed
Site P1,2When, the influence to workpiece maximum machining deformation is most sensitive, thereby determine that the 1st successive step should along figure Y-axis shown in arrow
Direction mobile positioning point P1,2, position is interfered by the Y-direction of machining path and adjacent positioned point to be constrained.After adjustment, calculate again most
Big machining deformation, is still located atPlace, and anchor point P1,2Influence to maximum machining deformation is still most sensitive, therefore the 2nd step
Adjustable strategies are identical with the 1st successive step；Other processes are similar.After special 27th successive step, maximum machining deformation is located atPlace, and by anchor point P8,1、P10,1Opposite P8,2、P10,2Y-direction interference constraint, can not continue along Y-axis running fix
Point reduces machining deformation, therefore enters adjusting stage II, and the strategy along X-direction adjustment anchor point distribution is selected to continue optimum position
Point layout.
After Fig. 9 shows access into adjusting stage II, anchor point P8,1、P8,2Movement pair in the direction of the arrowThe change at place
Shape influence it is most sensitive, show the 28th successive step should along figure the P of X-direction mobile positioning point shown in arrow8,1、P8,2.After adjustment,
Maximum machining deformation is located at known to calculating againPlace, based on the principle of " preferentially adjusting anchor point along Y direction ", meter
Calculate anchor point P1,2、P2,1、P3,2And P4,1Along Y direction moving influenceThe susceptibility of the maximum machining deformation in place, it is known that
P4,1For most sensitive anchor point, therefore the 29th successive step P of Y direction mobile positioning point shown in arrow along figure4,1, other process classes
Seemingly.After special 30th successive step, maximum machining deformation is located atPlace, the Y-direction by anchor point movement interfere constraint, can not
Along Y direction mobile positioning point P8,1、P10,1、P8,2And P10,2Reduce maximum machining deformation, therefore enter adjusting stage III, selects edge
The strategy that X-direction adjusts anchor point distribution continues optimum position point layout.
After Figure 10 shows access into adjusting stage III, especially during the adjustment of the 33rd~37 step, always to anchor point
P1,2Position be adjusted, but direction is alternately opposite, and corresponding maximum machining deformation position is in figureBetween vibrated, show can not to continue to reduce along Y direction mobile positioning point maximum processing and become
Therefore shape is jumped out after the 37th step and moves adjustment programme along Y-axis, into moving along the x-axis adjustment programme, therefore started with the 38th step
Adjusting stage IV.Similar oscillatory process is equally present in adjusting stage V, VI, VIII, IX, X, XII.
In final adjustment stage XIII, as shown in figure 11, the 97th~101 successive step process X-axis shown in arrow along figure
Direction mobile positioning point P8,1、P8,2, and maximum machining deformation position existsWithBetween vibrate, show at this time
It can not continue to reduce maximum machining deformation along X-direction adjustment anchor point, while by the Y-direction of machining path and adjacent positioned point
Interference constraint, anchor point can not also continue to be moved along Y-axis to reduce maximum machining deformation.Therefore, under the premise of existing constraint
The distribution of anchor point is determined, and machining path maximum machining deformation is 0.6694mm, is inPlace.
The machining deformation of each discrete point of machining path, very bright before and after Figure 12 optimizes than right workpiece anchor point initial layout
Aobvious, the machining deformation in path 1 greatly reduces after optimization, and the machining deformation in path 2 is held essentially constant, and main cause exists
In：Compared with path 1, the positioning dot density bigger around path 2.Therefore, maximum machining deformation does not appear at path 2, and
Anchor point around the non-selected adjustment machining path 2 of optimization process.Meanwhile maximum machining deformation and follow dynamic stiffness with adjustment time
Several variation tendencies is as shown in figure 13, and maximum distortion substantially increases workpiece process than reducing 34.5% before optimization
Rigidity.
(5) more anchor points optimization layout of workpiece is corrected again.
1) mode experiment is designed：According to more anchor points optimization layout of workpiece shown in Figure 11, the mode of work clipping system is built
Test system, as shown in figure 14, mainly by work clipping system, 086D50 type PCB power hammer, piezoelectric type ICP three-dimensionals acceleration transducer,
LMS SCADAS III multichannel numbers are adopted, Test.Lab model analyses software and computer form.Using power hammer hammering in experiment
Method carries out external drive to entire work grasping system, and then by multi-measuring point picking up work piece dynamic characteristic response signal, and to survey
Test system completes filtering, amplification and the parameter identification of pulse signal wave, and the final workpiece that obtains is under corresponding more anchor point layouts
Characteristics of mode parameter.
2) characteristics of mode of work clipping system is extracted：As shown in figure 15, it can be seen that by 1 rank Mode Shape of workpiece：1. in width
Direction, workpiece itself have preferable rigidity, although the cantilevered out part of lower edge is long, generate bending vibration deformation compared with
It is weak；2. in length direction, although workpiece extension is shorter, itself compared to width direction rigidity it is weaker, and produce compared with
Big bending vibration deformation；3. being vertically bent without supporting zone, generation among workpiece.In addition, shaking to two ranks before workpiece
Type feature is described, as shown in table 2.
2 curved surface thin-wall part 1 of table, the description of 2 first order modes
3) more anchor points optimization layout of workpiece is corrected：According to test result described in table 2, the workpiece entirety vibration shape is " bending+torsion
It is bent ", if only arranging a pair of of auxiliary positioning point, flexural deformation can only be inhibited.Therefore, two pairs of auxiliary positionings of arrangement may be selected
Point, flexural deformation and torsional deflection to workpiece can play inhibiting effect.Auxiliary positioning is counted out and method for determining position
It is as follows：1. determine the bending two ends deformation range of Workpiece length Direction distortion curve, select the centre position in the deformation section for
Auxiliary positioning point position.2. the characteristics of deformation curve midpoint is deformed into zero in the width direction according to workpiece, auxiliary positioning point position
It can be placed between zero deformation and maximum distortion.
For the multipoint positioning fixture system used in the example, although its structure cannot be satisfied above-mentioned auxiliary branch
The implementation of support point adding procedure, but can be by the positioning on No. 2 ram of outermost of the final anchor point layout of workpiece shown in Figure 11
Point P2,1、P2,2Entirety is moved to the left, and also be can reach and is subtracted with adding auxiliary positioning point to the larger position of edge vibration deformation tendency
The purpose of weak assembly parts distorted trend.Obviously, the amendment of above-mentioned anchor point layout certainly will will lead to 1 lower left side right angle of machining path
The deformation in region increases, but also plays vibration suppression effect simultaneously, and does not adjust anchor point P2,1、P2,2When inherent frequency of workpiece phase
Than 1 rank intrinsic frequency has been increased to 66.607Hz.In addition, although the vibration shape at position changes little, its edge among workpiece
The vibration shape has larger change, its evolution of deformation is the warpage of lower-left corner after adjustment, preferably inhibits vibration.
Claims (1)
1. a kind of localization method of large scale weak separation Thin-shell workpiece, includes the following steps：
1) it selects chucking power with machining deformation to ensure workpiece positioning completely index the most direct and important, and determines its target
Value range；
2) anchor point quantity needed for workpiece is determined：Its finished surface is directly divided into several machining areas along work pieces process path
With non-processing region, to meet chucking power demand as target, and based on workpiece configurations positioning accuracy, anchor point total resources and determine
The constraints of geometrical interference between site preferentially adds anchor point in machining area, anchor point quantity needed for workpiece is determined with this；
3) the more anchor point initial layouts of workpiece are searched for：Under the premise of ensuring workpiece reliable retention, using following each processing district of workpiece
The mode of domain maximum positioning error location arrangements anchor point, targetedly its different machining area position error of emphasis prevention and control,
Its disturbance to processing quality is further suppressed, thus to obtain more anchor point initial layouts of workpiece；
4) the more anchor point initial layout optimisation strategies of workpiece are designed：It is inspired by plant growth competition rule, parsing workpiece positioning
Internal association between point layout and machining deformation, the susceptibility expression of structure work pieces process deformation relative positioning point layout change
Formula, to reduce machining deformation as target, the most sensitive adjustment direction of search workpiece anchor point distribution positions more in this, as workpiece
The Optimal Decision-making of point initial layout, the susceptibility expression formula that the work pieces process deforms relative positioning point layout change are：
In formula, SxIndicate that the machining deformation of workpiece moves the susceptibility of increment with anchor point along tooling X-axis while Moving Unit；Pi
Indicate space coordinate square of each slide positioning unit end anchor point in tooling coordinate system on workpiece No. i-th ram of positioning tool
Battle array, i=1~m, m indicate the quantity of tooling upper ram；Pi+With f (Pi+) indicate each on workpiece No. i-th ram of positioning tool respectively
Slide positioning unit end anchor point moves increment Delta p along tooling X-axis positive direction Moving UnitxAfterwards all anchor points layout and
The maximum machining deformation of workpiece under the layout；Pi-With f (Pi-) indicate that each slide is fixed on workpiece No. i-th ram of positioning tool respectively
Bit location end anchor point moves increment Delta p along tooling X-axis negative direction Moving UnitxAll anchor points layout afterwards and the layout
The maximum machining deformation of lower workpiece；SyIndicate that the machining deformation of workpiece moves increment with anchor point along tooling Y-axis Moving Unit
Susceptibility；Pi,j+With f (Pi,j+) jth slide positioning unit end anchor point on workpiece No. i-th ram of positioning tool is indicated respectively
Increment Delta p is moved along tooling Y-axis positive direction Moving UnityThe maximum processing of workpiece under all anchor points layout and the layout afterwards
Deformation；Pi,j-With f (Pi,j-) jth slide positioning unit end anchor point edge on workpiece No. i-th ram of positioning tool is indicated respectively
Tooling Y-axis negative direction Moving Unit moves increment Delta pyThe maximum processing of workpiece becomes under all anchor points layout and the layout afterwards
Shape；
5) optimize the more anchor point initial layouts of workpiece：Workpiece anchor point layout optimization process is expressed as being intended to reduce machining deformation
More anchor points coordinate and optimize problem, pass through the inner link parsed between optimal objective value and restrained boundary, construction adjustment workpiece
Anchor point layout approaches the Optimizing Flow of minimum process deformation, and the optimization to the more anchor point initial layouts of workpiece is realized with this；
6) the more anchor point initial layouts of workpiece are corrected：Mode experiment is designed, test work clipping system is under more anchor points optimization layout
Modal parameter, and then according to modal frequency and the vibration shape, the more anchor points layouts of workpiece after optimization are finely adjusted, or continue to add
Add auxiliary positioning point, inhibits processing to vibrate with this, and further increase workpiece processing quality.
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| CN104097098A (en) * | 2014-07-07 | 2014-10-15 | 西安工业大学 | Multipoint positioning method for large curved-surface thin-walled workpieces |
| CN104476109A (en) * | 2014-09-25 | 2015-04-01 | 北京航星机器制造有限公司 | Skin structure accurate positioning machining method |
| CN104537172A (en) * | 2014-12-24 | 2015-04-22 | 天津大学 | Method for controlling hole group composite position degree error through optimizing clamp layout |
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| CN104097098A (en) * | 2014-07-07 | 2014-10-15 | 西安工业大学 | Multipoint positioning method for large curved-surface thin-walled workpieces |
| CN104476109A (en) * | 2014-09-25 | 2015-04-01 | 北京航星机器制造有限公司 | Skin structure accurate positioning machining method |
| CN104537172A (en) * | 2014-12-24 | 2015-04-22 | 天津大学 | Method for controlling hole group composite position degree error through optimizing clamp layout |
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| Title |
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| Multi-Point Positioning Method for Flexible Tooling System in Aircraft Manufacturing;Chunqing Liu等;《Proceedings of the ASME 2012 International Mechanical Engineering Congress and Exposition》;20121231;第113-117页 * |
| 飞机薄壁件多点柔性定位变形控制寻优算法;刘春青等;《上海交通大学学报》;20130831;第1191-1197页 * |
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